Force-sensing net

ABSTRACT

In exemplary implementations of this invention, a basketball net or flat net measures the translational kinetic energy of a ball that passes through an aperture in the net or impacts the net. The net includes one or more electrically conductive cords, which have a resistance that varies depending on the degree to which the cord is stretched. From sensor measurements, a processor determines: (a) instantaneous rate of change of resistance, and (b) duration of a time period that begins when resistance exceeds a baseline (with hysteresis). In the case of a basketball net, a processor may calculate the translational kinetic energy of the ball as equal to a sum of two terms. The first term is inversely proportional to the square of the duration; the second is proportional to the square of the integral of the instantaneous rate of change of resistance over the time period.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/734,182, filed Jan. 4, 2013 (the “182 Application”), which claims thebenefit of U.S. Provisional Application No. 61/583,120, filed Jan. 4,2012 (the “120 Application”), and of U.S. Provisional Application No.61/603,013, filed Feb. 24, 2012 (the “013 Application”). The entiredisclosures of the 182 Application, 120 Application and 013 Applicationare herein incorporated by reference.

FIELD OF THE TECHNOLOGY

The present invention relates generally to nets.

SUMMARY

In exemplary implementations of this invention, a net is configured tomeasure the translational kinetic energy of a ball that passes throughan aperture in the net or that impacts the net. For example, the net maybe a basketball net or a flat net.

The net includes one or more electrically conductive cords. These cordsmay, or may not, be aligned with conventional cords in the net. Each ofthese electrically conductive cords has an electrical resistance thatvaries depending on the degree to which the cords are stretched.

At least one sensor measures change in resistance of the components as aball impacts (or passes through an aperture in) the net. From thesemeasurements, at least two parameters can be determined: (a)instantaneous rate of change of resistance, and (b) duration of a timeperiod that begins when resistance exceeds a baseline plus a thresholdand ends when resistance is less than a baseline minus a threshold.

At least one processor performs an algorithm that calculates anapproximation of the translational kinetic energy of the ball. Theapproximation is equal to a sum of two terms. The first term isinversely proportional to the square of the duration; the second term isproportional to the square of the integral of the instantaneous rate ofchange of resistance over the time period. In the case of a sampleddigital system with a sufficiently fast sampling rate, the integral maybe approximated by a sum of the samples during the duration of theperiod.

The velocity of a ball that impacts or passes through a basketball nethas both a vertical and horizontal component, each of which have a verydifferent effect on the stretch (and thus resistance) of the conductivecords. This invention can determine both the horizontal and verticalcomponents, based on sensor measurements from a single conductive cord.In the algorithm described above, the first term in the sum predominatesin the case of the vertical component of the velocity; the second termin the sum predominates in the case of the horizontal component.

If the net is a flat net, the net may have N electrically conductivecords oriented in a horizontal direction and M electrically conductivecords oriented in a vertical direction. Further, the flat net may haveN+M conventional cords aligned with the conductive cords. When a ballimpacts the flat net, the peak stretch occurs at an x, y positionapproximately equal to the intersection of two cords: the conductivecord with the greatest stretch (and thus greatest resistance) in thehorizontal direction and the conductive cord with the greatest stretch(and thus greatest resistance) in the vertical direction. In order tocalculate the translational kinetic energy of a ball that impacts theflat net, the processor identifies these two cords, and then performsthe above algorithm, using resistance measurements from one of these twocords.

However, in the flat net case, the first of the two terms in the sum ofterms may be set to zero. That is, in the flat net case, translationalkinetic energy may be well-approximated by using only the second termdescribed above (which is proportional to the square of the integral ofthe instantaneous rate of change of resistance over the time period).

The processor may also derive, in conjunction with calculating thekinetic energy: (i) the ball's speed; and (ii) a force that the ballapplies to the net, or that was applied to the ball.

The calculated kinetic energy or speed of the ball (or the force) may berendered by an output device in human-readable form.

This invention has many practical uses. For example, in the case of abasketball net, this invention may be used to measure the kinetic energyand speed of a basketball that is being dunked. Or, for example, in thecase of a flat net, this invention may be used to measure the kineticenergy and speed of a baseball or soccer ball that is kicked, hit, orthrown into the net.

The description of the present invention in the Summary and Abstractsections hereof is just a summary. It is intended only to give a generalintroduction to some illustrative implementations of this invention. Itdoes not describe all of the details of this invention. This inventionmay be implemented in many other ways.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a basketball net that includes a single electricallyconductive cord.

FIG. 2 shows a basketball net that includes multiple electricallyconductive cords.

FIG. 3 shows a flat net, in which electrically conductive cords form acrisscross pattern.

FIG. 4 shows a flowchart for determining (without hysteresis) thetranslational kinetic energy of a ball that impacts or passes through anet.

FIG. 5 shows a flowchart for determining (with hysteresis) thetranslational kinetic energy of a ball that impacts or passes through anet.

The above Figures illustrate some illustrative implementations of thisinvention, or provide information that relates to those implementations.However, this invention may be implemented in many other ways. The aboveFigures do not show all of the details of this invention.

DETAILED DESCRIPTION

In exemplary implementations of this invention, a basketball netincludes one or more segments of conductive cord whose resistancechanges with degree of stretch. For example, the resistance may increaseas the stretch increases. Examples of such material includecarbon-impregnated silicone cord and metalized textile threads andyarns.

In some cases, the conductive cords are roughly aligned with at leastsome of the conventional cords in the net. For example, the conductivecords may be inserted into a hollow conventional cord making up the net,or may be woven into the conventional cord itself.

By passing a low voltage and current through the conductive material andmeasuring the resistance over time (e.g., taking samples usinganalog-to-digital conversion circuitry), computing hardware associatedwith this net can calculate energy and speed of a basketball travelingthrough the net. Applications include training, toys that indicate theenergy and speed on a display, “dunk competitions,” and augmentedreality effects on television broadcasts driven by the data from thenet.

In exemplary implementations, the net is less expensive and more robustthan conventional approaches to measuring data about the ball (e.g.,photosensors or ultrasonic sensors) and doesn't require a physicalchange to the hoop or backboard other than providing electricalconnections to the net. If the basketball hoop is made of metal and thusconductive, it is preferable to arrange for the conductive segments andtheir electrical connections to be insulated from the hoop where thehoop contacts the net.

The conductive material can extend throughout the entire net or can beincorporated into one or more smaller sections.

FIGS. 1 and 2 show examples of basketball nets that are configured tomeasure the translational kinetic energy of a basketball that passesthrough the net. In FIG. 1, the net includes only one electricallyconductive cord 103. In FIG. 2, the net includes multiple electricallyconductive cords (e.g., 203, 205).

In the example shown in FIG. 1: (1) the net includes a singleelectrically conductive cord 103, the resistance of which depends on thedegree to which this cord is stretched; (2) the net also includesconventional cords 105; (3) the net is attached to a metal hoop 101; and(4) the electrically conductive cord 103 and leads 107, 109 areelectrically insulated from the metal hoop 101.

In the example shown in FIG. 3: (1) the net includes multipleelectrically conductive cords (e.g., 203, 205), the resistance of whichdepends on the degree to which this cord is stretched; (2) the net alsoincludes conventional cords 211; (3) the net is attached to a metal hoop201; and (4) the electrically conductive cords (e.g., 203, 205) andleads (e.g., 207, 209) are electrically insulated from the metal hoop201.

This invention may be implemented as a flat net that can measuretranslational kinetic energy and velocity of a ball hit or pitched intoit (as in baseball or tennis). In some implementations, the flat net isdivided electrically into multiple zones and can also measure positionof the ball's impact (e.g., for determining whether a practice baseballpitch would have been a strike) through comparison of the resistances ofthe various segments over time. These different resistive segments maybe measured simultaneously or may be scanned rapidly in atime-multiplexed arrangement.

FIG. 3 shows an example of a flat net 301. The flat net is attached to ametal frame 303. The flat net includes a crisscross pattern ofelectrically conducting cords, some of which (e.g. 309, 311) areoriented vertically and some of which (e.g., 313, 315) are orientedhorizontally. The electrically conducting cords are generally alignedwith a crisscross pattern of conventional cords (e.g., 305, 307), andare electrically insulated from each other and the metal frame.

Other arrangements besides those shown in FIGS. 1, 2 and 3 may be usedinstead, and may prove advantageous in various applications.

In exemplary implementations of this invention, a basketball netincorporates one or more segments of conductive fiber or cord whoseresistance changes with degree of stretch. This resistance is measured.The resistance measurement is used for computing energy of a basketballthat passes through a basketball net (e.g., by dunking).

The passage of a ball is detected by setting a threshold (withhysteresis) depending on the baseline resistance of the net. Thus, twoparameters are available: instantaneous increase in resistance and timeduration of the increase (effectively the duration of the ball's contactwith the net). Depending on the trajectory of the ball its velocity canhave a vertical and a horizontal component, and each of these has a verydifferent effect on the stretch (and thus resistance) over time, leadingto a dunk of equal energy producing very different readings when it hitsthe net at different angles.

One possible solution is to segment the net and compare the stretchapplied to different segments, but in some situations it is impracticalto have more than one set of electrical connections to the net.

Thus, in preferred embodiments of this invention, separate resistancereadings for different segments of the net are not taken. Instead, asingle resistance reading (at any given time) is taken, from which theproblem is solved.

In exemplary implementations of this invention, a basketball net issufficiently tightly constructed that a ball going through verticallywill experience some friction with the net and produce a measurablestretch. Such a vertical velocity will result in the ball being incontact (and the resistance reading changing) for a time interval thatdecreases with the ball's velocity. The energy associated with thisvelocity is proportional to the square of the velocity (and thus to thereciprocal of the square of the duration).

A ball traveling through the net but hitting the net mostlyhorizontally, on the other hand, has an energy proportional to thesquare of the integral of the change in resistance over the timeduration.

Thus in the general case the translational kinetic energy iswell-approximated as the sum of two terms:energy≈k ₁/duration² k ₂ [∫ΔRdt]²  (Equation 1)where R is resistance, t is time, and k₁ and k₂ are constants that aredetermined by calibrating experiments.

The first term dominates for a ball moving quickly through the netvertically, and the second term dominates for a ball that hits the sideof the net and remains inside the net for a longer period. In the caseof a sampled digital system the integral is approximated by a sum ofsamples during the duration (assuming a high enough sampling rate toestimate the duration with reasonable precision).

In exemplary implementations, the energy of a ball passing through aforce-sensing net (e.g., by dunking) may be calculated using Equation 1.The algorithm shown in FIG. 1 may be employed for these calculations.

One or more processors may be used for these calculations. (For example,rectangles 123, 223, 323 in FIGS. 1, 2, 3, respectively, each representone or more processors). At least some of the processors may be remotefrom the force-sensing net. The processors may be connected by wired orwireless connection (1) to a sensor (e.g., 121, 221, 321) for measuringresistance in the force-sensing net, and (2) to an output device (e.g.125, 225, 325) for rendering the calculated energy or speed in ahuman-readable format.

This invention may be implemented as a flat, two-dimensional net, whereN sensor circuits in one dimension are insulated from M sensor circuitsin the other dimension, and where N+M resistance readings can be takenby scanning along each dimension. The (x, y) coordinates of the point ofcontact by the ball can be estimated as the locations of the peakresistance values (once an above-threshold value is detected) along eachdimension. Interpolation (such as bicubic) can be applied if a finerlocation estimate is desired.

In some implementations, sensors take the N+M resistance readings forthe flat net simultaneously. Alternately, the N+M resistance readingsmay be taken sequentially.

In the flat net case, the same energy-estimating algorithm (Equation 1and FIG. 1) can be used. The algorithm is applied to a single sensorcircuit in one dimension that first registered the above-thresholdvalue. In the flat net case, however, the first proportionality constant(k₁) in Equation 1 may be set to zero. In other words, in the flat netcase, the translational kinetic energy may be well approximated by thesecond term on the right in Equation 1. This second term is proportionalto the square of the integral of the change in resistance over the timeduration.

Even in the round-net case (e.g., a basketball net), it may suffice insome circumstances to calculate only one of the two terms in Equation 1:i.e., to set one of the two proportionality constants (k₁ and k₂) inEquation 1 to zero. Whether such an approach would suffice may depend onthe expected trajectory of the ball and the orientation of the net. Forexample, if a basketball is expected to pass vertically through a net(on a straight-down dunk), using only the first term on the right(k₁/duration²) in Equation 1 may achieve a close approximation.Likewise, if the basketball is expected to strike the basketball netalmost horizontally, then using only the second term on the right(k₂[∫ΔRdt]²) in Equation 1 may suffice.

Because the sensor material may not respond uniformly throughout atwo-dimensional net (e.g., the ball may create less stretch near thesupported edges of the net than in the center) the detection thresholdsor the constants in the energy-calculation algorithm may be varied as afunction of position, based on calibrated measurements.

FIG. 4 shows a flowchart for determining (without hysteresis) thetranslational kinetic energy of a ball that impacts or passes through anet.

FIG. 5 shows a flowchart for determining (with hysteresis) thetranslational kinetic energy of a ball that impacts or passes through anet.

In some alternative implementations, the resistance of the electricallyconductive material decreases as stretch increases (rather thanincreasing as stretch increases). In those alternative implementations,the above algorithm and flow charts are modified accordingly. Forexample, in those implementations, the time period measured may beginwhen resistance is less than a baseline minus a first amount and endwhen resistance exceeds the baseline plus a second amount

Definitions and Clarifications

Here are a few definitions and clarifications. As used herein:

The terms “a” and “an”, when modifying a noun, do not imply that onlyone of the noun exists.

The term “comprise” (and grammatical variations thereof) shall beconstrued broadly, as if followed by “without limitation”. If Acomprises B, then A includes B and may include other things.

The term “cord” shall be construed broadly. For example, one or morefibers may comprise a cord.

The term “e.g.,” means including without limitation.

The fact that an “example” or multiple examples of something are givendoes not imply that they are the only instances of that thing. Anexample (or a group of examples) is merely a non-exhaustive andnon-limiting illustration.

Unless the context clearly indicates otherwise: (1) a phrase thatincludes “a first” thing and “a second” thing does not imply an order ofthe two things (or that there are only two of the things); and (2) sucha phrase is simply a way of identifying the two things, respectively, sothat they each can be referred to later with specificity (e.g., byreferring to “the first” thing and “the second” thing later). Forexample, unless the context clearly indicates otherwise, if an equationhas a first term and a second term, then the equation may (or may not)have more than two terms, and the first term may occur before or afterthe second term in the equation. A phrase that includes “a third” thing,a “fourth” thing and so on shall be construed in like manner.

The terms “horizontal” and “vertical” shall be construed broadly. Forexample, “horizontal” and “vertical” may refer to two arbitrarily chosencoordinate axes in a Euclidian two dimensional space.

The term “include” (and grammatical variations thereof) shall beconstrued broadly, as if followed by “without limitation”.

The term “or” is inclusive, not exclusive. For example “A or B” is trueif A is true, or B is true, or both A or B are true. Also, for example,a calculation of “A or B” means a calculation of A, or a calculation ofB, or a calculation of A and B.

A parenthesis is simply to make text easier to read, by indicating agrouping of words. A parenthesis does not mean that the parentheticalmaterial is optional or can be ignored.

The phrase “to render in human readable form” (and other phrases ofsimilar import) shall be construed broadly. For example, it includesoutputting audio or visual stimuli that are perceivable by unaided humanperception.

Variations:

This invention may be implemented in many different ways. Here are somenon-limiting examples.

This invention may be implemented as apparatus comprising incombination: (a) a net; (b) at least one sensor; and (c) at least oneprocessor; wherein: (i) the net includes one or more components, each ofwhich components comprises a material that has an electrical resistancethat varies depending on the extent to which the material is stretched,(ii) the at least one sensor is configured to take measurements ofchanges in electrical resistance of each of the one or more components,respectively, (iii) the at least one processor is configured (A) toperform a computation to calculate, based at least in part on themeasurements, a calculated value indicative of the translational kineticenergy of a ball that strikes or passes through the net, and (B) tooutput signals to cause an output device to render the calculated valuein a human-readable form; and (iv) the calculated value is in a range,which range is the range of values that may be outputted by thecomputation, and which range includes more than two values. Furthermore:(1) the net may comprise a basketball net; (2) the net may comprise aflat net; (3) the computation may include a calculation of aninstantaneous rate of change in resistance; (4) the computation mayinclude a calculation of duration of a time period, which period startswhen resistance exceeds a baseline plus a first amount and ends whenresistance is less than the baseline minus a second amount; (5) thefirst and second amounts may be different; (6) the computation mayinclude one or more calculations of (a) an instantaneous rate of changein resistance, or (b) a duration of a time period, which period startswhen resistance exceeds a baseline plus a first amount and ends whenresistance is less than the baseline minus a second amount; (7) thecomputation may include a mathematical operation involving a first termthat is inversely proportional to the square of the duration, or that isproportional to the square of speed of the ball; (8) the computation mayinclude a mathematical operation involving a second term that isproportional to the square of the integral of the change in resistanceover the time period; (9) the computation may include approximating theintegral by performing a calculation that includes computing a sum ofsamples taken during the time period; (10) the first term may beproportional to a first constant and the second term may be proportionalto a second constant; (11) a computation for a single impact of the ballon the net may be based on measurements readings from a singlecomponent; (12) (i) the net may be a flat net, (ii) the one or morecomponents may include N elongated components oriented in along a firstdirection and M elongated components oriented along a second direction,(iii) the at least one sensor may be configured to measure resistance ineach of the N+M components respectively, (iv) the at least one processormay be configured to identify a particular component that exhibitsmaximum resistance out of the M components, or out of the N components,or out of the N+M components, during the time period, and (v)measurements of resistance for the particular component taken duringtime period may be either the sole measurements of resistance takenduring the time period that are inputted into the computation, or may beweighted more heavily in the computation than measurements of resistanceof other components taken during the time period; (13) the at least onesensor may be configured to measure resistance in each of the N+Mcomponents simultaneously; (14) the at least one sensor may beconfigured to measure resistance in each of the N+M componentssequentially; (15) the computation may further include a calculation ofa calculated speed of the ball, and the processor may be furtherconfigured to output signals to cause the output device to render thecalculated speed in a human-readable form; and (16) the electricalresistance of the material may decrease as stretch of the materialincreases, and the computation may include one or more calculations ofan instantaneous rate of change in resistance or a duration of a timeperiod, which period starts when resistance is less than a baselineminus a first amount and ends when resistance exceeds the baseline plusa second amount.

This invention may be implemented as a method comprising in combination:(a) using at least one sensor to take measurements of changes inelectrical resistance of each of the one or more components, whichcomponents are part of a net and each comprise a material that has anelectrical resistance that varies depending on the extent to which thematerial is stretched; and (b) using at least one processor (i) toperform a computation to calculate, based at least in part on themeasurements, a calculated value indicative of the translational kineticenergy of a ball that strikes or passes through the net, and (ii) tooutput signals to cause an output device to render the calculated valuein a human-readable form; wherein the calculated value is in a range,which range is the range of values that may be outputted by thecomputation, and which range includes more than two values. Furthermore:(1) the computation may include a calculation of an instantaneous rateof change in resistance; and (2) the computation may include acalculation of duration of a time period, which period starts whenresistance exceeds a baseline plus a first amount and ends whenresistance is less than the baseline minus a second amount.

CONCLUSION

It is to be understood that the methods and apparatus that are describedherein are merely illustrative applications of the principles of theinvention. Numerous modifications may be made by those skilled in theart without departing from the scope of the invention.

What is claimed is:
 1. An apparatus comprising in combination: (a) a netthat has an aperture and that includes one or more cords, which one ormore cords (i) are stretchable, (ii) are electrically conductive, (iii)have an electrical resistance that varies depending on the extent towhich the one or more cords are stretched, and (iv) are positioned suchthat the one or more cords stretch when a ball passes through theaperture; (b) at least one sensor for measuring the electricalresistance; and (c) at least one processor for performing a computationthat includes (i) calculating a duration of a time period, which periodstarts when the electrical resistance exceeds a baseline plus a firstamount and ends when the electrical resistance is less than the baselineminus a second amount, and (ii) calculating, based at least in part onthe duration of the time period, the translational kinetic energy of theball that passes through the aperture.
 2. The apparatus of claim 1,wherein the net comprises a basketball net.
 3. The apparatus of claim 1,wherein the net is tubular.
 4. The apparatus of claim 1, wherein thecomputation includes calculating an instantaneous rate of change of theresistance.
 5. The apparatus of claim 1, wherein the first amount isdifferent than the second amount.
 6. The apparatus of claim 1, whereinthe computation includes a mathematical operation involving a term thatis inversely proportional to the square of the duration.
 7. Theapparatus of claim 1, wherein the computation also includes: (a)calculating an estimate of an integral of change in the resistance, bycalculating a sum of samples; and (b) calculating the translationalkinetic energy as proportional to the square of the estimate of theintegral.
 8. The apparatus of claim 7, wherein the computationcalculates the translational kinetic energy as inversely proportional tothe square of the duration and as proportional to the square of theestimate of the integral.
 9. The apparatus of claim 1, wherein thetranslational kinetic energy is calculated as a variable that has arange of more than two values.
 10. A method of estimating translationalkinetic energy of a ball passing through an aperture in a net, which netincludes one or more cords that are stretchable, electrically conductiveand have an electrical resistance that varies depending on the extent towhich one or more cords are stretched, which method comprises, incombination: (a) measuring the electrical resistance by at least onesensor; and (b) performing a computation by at least one processor,which computation includes (i) calculating a duration of a time period,which period starts when the electrical resistance exceeds a baselineplus a first amount and ends when the electrical resistance is less thanthe baseline minus a second amount, and (ii) calculating, based at leastin part on the duration of the time period, the translational kineticenergy of the ball that passes through the aperture in the net, whereinthe one or more cords are positioned such that the one or more cordsstretch when the ball passes through the aperture.
 11. The method ofclaim 10, wherein the net comprises a basketball net.
 12. The method ofclaim 10, wherein the net is tubular.
 13. The method of claim 10,wherein the computation includes calculating an instantaneous rate ofchange of the resistance.
 14. The method of claim 10, wherein the firstamount is different than the second amount.
 15. The method of claim 10,wherein the computation includes a mathematical operation involving afirst term that is inversely proportional to the square of the duration.16. The method of claim 10, wherein the computation also includes: (a)calculating an estimate of an integral of change in the resistance, bycalculating a sum of samples; and (b) calculating the translationalkinetic energy as proportional to the square of the estimate of theintegral.
 17. The method of claim 16, wherein the computation calculatesthe translational kinetic energy as inversely proportional to the squareof the duration and as proportional to the square of the estimate of theintegral.
 18. The method of claim 10, wherein only one measurement ofthe resistance is taken at any given time.
 19. The method of claim 10,wherein the resistance increases as stretch of the one or more cordsincreases.
 20. The method of claim 10, wherein the translational kineticenergy is calculated as a variable that has a range of more than twovalues.